A fogorvos azért készít röntgenfelvételt, hogy lássa az őrlőfogat.

This is a very common Hungarian pattern for expressing purpose.

• azért = for that reason / for that purpose
• hogy = that / so that

Together, azért ... hogy means something like:

• so that
• in order to
• for the purpose of

So:

• A fogorvos azért készít röntgenfelvételt, hogy lássa az őrlőfogat. = The dentist takes an X-ray so that he/she can see the molar.

Hungarian often uses this structure where English might simply use to + verb.

Because after hogy in a purpose clause, Hungarian normally uses the imperative/subjunctive form of the verb, not the ordinary present tense.

So here:

• látja = he/she sees it
• lássa = so that he/she may see it / can see it

In English, this distinction is often hidden, because we usually translate it naturally as can see or see.

So:

• hogy lássa az őrlőfogat literally means something like so that he/she may see the molar

This is one of the most important things to notice in this sentence.

Because lássa is the 3rd person singular definite imperative/subjunctive form of lát.

Hungarian verbs can show whether their object is:

• definite: a specific thing
• indefinite: a non-specific thing

Here the object is az őrlőfogat = the molar, which is definite, so the verb also uses the definite form:

• lássa = let him/her see it / so that he/she may see it

If the object were indefinite, the form would be different.

So the sentence is teaching you two things at once:

1. the purpose clause after hogy
2. the definite conjugation

Because it is the direct object of the verb készít.

In Hungarian, direct objects usually take the accusative ending -t.

• röntgenfelvétel = X-ray image / radiograph
• röntgenfelvételt = an X-ray image, as the object

So:

• készít röntgenfelvételt = takes/makes an X-ray

The -t is one of the most common Hungarian case endings, and you will see it constantly.

Because Hungarian often adds a linking vowel before the accusative -t when a word ends in a consonant and the form would otherwise be awkward.

• őrlőfog = molar
• őrlőfogat = molar, as the direct object

So this is:

• base noun: őrlőfog
• accusative ending: -at

This is completely normal in Hungarian. The accusative is not always just a bare -t attached directly.

Compare the same pattern with other nouns:

• kar → kart
• híd → hidat
• fog → fogat

Since őrlőfog ends in fog, it follows that same pattern.

Because röntgenfelvételt is being used indefinitely, while az őrlőfogat is definite.

• röntgenfelvételt készít = takes an X-ray
• az őrlőfogat = the molar

In Hungarian, indefinite singular nouns often appear without a word corresponding to English a/an.

So English says:

• takes an X-ray

But Hungarian often simply says:

• röntgenfelvételt készít

If you said egy röntgenfelvételt, that would put more emphasis on one X-ray.

They are the same definite article: the.

Hungarian has two forms:

• a before a consonant sound
• az before a vowel sound

So here:

• a fogorvos because fogorvos starts with f
• az őrlőfogat because őrlőfogat starts with ő, a vowel

This is purely a sound-based rule, similar to how English has a and an.

készít literally means make, prepare, or produce.

In Hungarian, the natural expression is:

• röntgenfelvételt készít = literally make/prepare an X-ray image = naturally in English take an X-ray

Languages often use different everyday verbs in these situations. English says:

• take a photo
• take an X-ray

Hungarian often says:

• fényképet készít = take a photo
• röntgenfelvételt készít = take an X-ray

So this is not a strange or overly literal wording in Hungarian; it is normal usage.

It is a compound word:

• fog = tooth
• orvos = doctor

So fogorvos literally means tooth doctor, which is the normal Hungarian word for dentist.

Hungarian makes a lot of compound nouns like this, so this is a useful word-building pattern to notice.

Because Hungarian often leaves the subject unstated when it is clear from the context.

In this sentence, the main clause subject is:

• A fogorvos = the dentist

Then the purpose clause is:

• hogy lássa az őrlőfogat = so that he/she can see the molar

The understood subject of lássa is normally the same person as in the main clause, unless Hungarian explicitly says otherwise.

If the sentence wanted to say that someone else is supposed to see it, it would usually name that person:

• ...hogy a beteg is lássa... = ...so that the patient can see it too...

So by default, we understand that the dentist is the one seeing the molar.

Hungarian word order is fairly flexible, but different orders can change the focus or emphasis.

The given sentence is natural and emphasizes the purpose clearly:

• A fogorvos azért készít röntgenfelvételt, hogy lássa az őrlőfogat.

A slightly simpler version is also possible:

• A fogorvos röntgenfelvételt készít, hogy lássa az őrlőfogat.

This still means basically the same thing, but azért ... hogy makes the purpose relationship more explicit.

So the word order is not completely rigid, but the sentence you were given is a very standard and useful pattern to learn.

Yes. In this kind of sentence, Hungarian often does not need a separate word for can the way English does.

• hogy lássa literally means something like so that he/she may see
• In natural English, that is often best translated as so that he/she can see

So the sense of ability/opportunity/purpose comes from the whole construction, not necessarily from a separate verb like can.

Hungarian does have a verb suffix for ability in many contexts, but here it is not needed. The purpose clause already expresses the intended result clearly.